Model of an unglazed photovoltaic thermal collector based on standard test procedures

Transcription

1 Model of an nglazed photovoltaic thermal collector based on standard test procedres Martin Stegmann, Erik Bertram, Gnter Rockendorf, Stefan Janßen Institt für Solarenergieforschng Hameln/Emmerthal (ISFH) Am Ohrberg, 386 Emmerthal (Germany); tel.: 55/ ; janßen energieplanng, Hohenzollernstraße 5, 36 Hannover (Germany). Introdction Existing PVT collector models are in general sing physical balance and transfer eqations, ths they are basing on the design data. Frthermore most of the models are simlating glazed PVT collectors. This paper presents a new model for nglazed liqid cooled PVT collectors that is based on the combination of parameters reslting from conventional thermal and electrical performance measrement data and their characteristic crves, which are obtained in standard test procedres. The thermal performance parameters are taken from a collector test according to EN 975-, while for the PV part, the effective solar cell model has been chosen, which ses reslts from a test according to EN Hence, only experimental performance parameters from established test methods are reqired to describe the complete PVT collector performance. In addition to this characteristic crve modelling, a physical approach is implemented for describing the condensation effects. Frthermore, the model takes the internal heat transfer coefficient between PV cells and flid into accont. This coefficient may be derived from the thermal performance parameters. The model has been transferred into the simlation program TRNSYS and tested against shortterm measrements on a test roof and validated against measrements in a 4 m² PVT collector field over the period of one year. The work presented in this paper has been realized within the project Solar heat spply for bildings with nglazed photovoltaic thermal collectors, borehole heat exchangers and heat pmps. In the research project heat spply systems for bildings with heat pmp and borehole heat exchanger are investigated. In typical systems the borehole heat exchanger temperatre decreases within the first years of operation. In conseqence, the efficiency of the system is decreasing and more electrical energy is needed to deliver the reqired heat. To prevent this temperatre decrease a solar thermal collector can be sed to inject solar thermal heat in the borehole and regenerate the earth temperatre. So, the temperatre level and the system s efficiency of the first year of operation are kept stable over the following years (Bertram, 9). In the system investigated an nglazed PVT collector has been selected, becase the needed collector otlet temperatre has not to be higher than 3 C. In addition to the improved heat pmp efficiency, the PV cells in the sed PVT collector are cooled. This increases their electrical efficiency. So, the se of PVT collectors in sch systems leads to a doble benefit, which redces the electrical energy demand for the heat pmp and increases the electrical yield in comparison to a not cooled PV power plant of identical size.. TRNSYS model for nglazed PVT collector Most of the existing models need design data for parameterization, which normally are nknown for the model operator. In the research project a simlation model was needed, that ses data from standard performance tests and incldes the effects of air speed, infrared radiation, thermal collector capacity and condensation on collector srface. As no appropriate model has been available to describe the dynamic behavior of an nglazed PVT collector in the necessary accracy, a new model had to be developed and implemented in TRNSYS... Model concept The core of the model concept is the combination of two characteristic performance models for an nglazed thermal collector and a standard PV modle. The thermal model is described by the measred performance The project Solare Gebäde-Wärmeversorgng mit nverglasten photovoltaisch-thermischen Kollektoren, Erdsonden nd Wärmepmpen für % Deckngsanteil (acronym BiSolar-WP), FKZ 3595, in cooperation with the company GEFGA, is fnded by the German Federal Ministry for the Environment, Natre Conservation and Nclear Safety (BMU) based on a decision of the German Federal Parliament. The content of this pblication is in the responsibility of the athors.

2 characteristic according to EN 975- and the electrical model is described by the empirical effective solar cell model (Wagner, 6), which only reqires standard performance test data of PV modles. Accordingly, only parameters from established performance tests and manfactre standard data sheets are needed for the dynamic calclation of the thermal heat flow rate and the electrical power. Both characteristics are interconnected via the incoming energy path and the PV cell temperatre... Thermal collector model The thermal collector model for nglazed solar thermal collectors is based on the characteristic performance model with a transient energy balance. The characteristic crve is described in EN The model takes the inflence of solar radiation (beam and diffse), air speed, flid, ambient and sky temperatre into accont. It also regards the redction of radiation by the incident angle modifier for thermal absorbers, the dynamic behavior and the effects of condensation on the collector srface. For the calclation of condensation the characteristic crve model was extended by a physical approach..3. Electrical model (PV modle) For the extension of the thermal model to a PVT collector model the particlarly sitable characteristic crve model effective solar cell model was sed, which is an empirical mathematical fnction valid for standard PV modles. Its inaccracy is reported to be less than % (Wagner, 6). It calclates the electrical power of a standard PV modle by sing the characteristics from the manfactrer s data sheet, the incident radiation and the cell temperatre. It therefore may be easily parameterized. The electrical power is calclated at the maximm power point (MPP) at the DC side..4. Combination of the two characteristic performance models The PVT collector model is composed by the combination of the models for the thermal and the electrical energy path. Fig.. shows the principle of the PVT collector model. G (T amb, T sky,, ) PVT-collector IAM el IAM therm IB f(t amb, T sky ) Q loss f(t amb, T sky, ) electrical model EN thermal model EN 975 T cell T glas P el f(g red, T cell ) Q cond f(t glas,,...) m in, T in m ot, T ot Q se f(g red4, T amb, ) Fig..: Combination of the two characteristic crve models for thermal collector and PV modle to a PVT collector model.5. Radiation splitting The incident radiation on collector srface G is redced by the incident angle modifier IAM el for the electrical PV modle (eq. ). Therefore the transversal and the longitdinal incident angle correction factors for beam radiation (eq. ) and the incident angle correction factor for diffse radiation is taking into accont. From the remaining radiation G red a fraction of the IAM- modified radiation is converted into electrical power P el. For the conversion into heat the available radiation G red is the difference between the incoming radiation G and the electrical power P el (eq. 3). Corresponding to the electrical IAM el redction, the radiation G red is redced by the incident angle modifier IAM therm for the thermal part of the model (eq.

3 and eq. ). Afterwards the radiation G red3 is redced by the infrared radiation balance IB to take into accont the long wave radiation emitted to the sky (eq. 4). So for the conversion into heat the net radiation G red4 is remaining (fig..). Gdif G (eq. ) dif G Θ + red G kθ,beam,eff,pv ( ) k dif,pv G G kθ, beam,eff,pv ( Θ ) kθ,beam,t,pv ( Θt ) kθ,beam,l,pv ( Θl ) (eq. ) P PV G red G (eq. 3) APVT ( G ( T 73.5K ) ) 4 ε G red 4 Gred3 + IR σ amb + α (eq. 4).6. Heat flow rate The conversion of the radiation G red4 into the sefl heat flow rate and the heat losses to the ambient air is calclated according to the qasi-dynamic model of EN It consists in a transient energy balance (eq. 5), that incldes the conversion of incoming radiation G red4 with heat losses against the ambient, the collector heat flow rate q se and the thermal collector capacity c eff. The model is completed by the term q, which represents the heat flow rate cased by condensation effects. c cond eff dt dt m red4 ( b ) ( b + b ) ( Tm Tamb ) + q cond q se G (eq. 5).7. Electrical power The electrical power of the PVT collector is calclated with the relative efficiency factor rel, which is the ratio of present efficiency to the efficiency at standard test conditions STC of the sed PV modle (eq. 6). The relative efficiency considers the cell temperatre, the amont of solar radiation and the PV modle properties (eq. 7). To describe the properties of the sed PV modle, the following axiliary parameters are needed. The imaginary photovoltaic resistance R PV and the physically variable temperatre voltage U T of the one diode model (Wagner, 6). P PV STC rel red η η G A (eq. 6) PVT ( ) U T,STC Gred R PV,STC I MPP,STC Gred η + + rel ct (Tcell TSTC ln U G U (eq. 7) MPP,STC STC MPP,STC GSTC.8. Cell temperatre To calclate the electrical power the cell temperatre is needed. Starting from the mean flid temperatre T m the cell temperatre T cell is calclated with the heat flow rate q se and the internal heat transfer coefficient int. This is valid nder the assmption, that the solar cell is the location, where most of the heat is prodced. qse T cell + T int m (eq. 8).9. Condensation effects Unglazed PVT collectors can collect sefl heat by condensation. Condensation on the oter srface of the PVT collector appears when the temperatre on the PVT collector srface is below the dew point temperatre T d of the ambient air. This additional condensation heat is transferred to the circlating flid. To calclate the srface temperatre of the PVT collector T glass a physical sbmodel with the network shown in fig.. is sed. In this sbmodel the effects of radiation to the sky and convective heat transfer to ambient air is considered. The srface temperatre determined according to eq. 5 is only sed for the calclation of the condensation heat flow rate (eq. 9). The collector heat flow rate itself is calclated by (eq. 5).

4 q radiation q glass radiatiion - T sky T cell glass - T glass q convection conv - T amb Fig..: Heat resistance network for the calclation of PVT collector srface temperatre (glass) R Δh [ p ( T ) p ( T )] L v m q cond Le conv s glass s d with m ~ /3 (eq. 9) RD pcl The convective heat transfer coefficient conv is calclated by an empirical fnction (eq. ). For the radiation to sky the heat transfer coefficient radiation is given by (eq. ) with the effective ambient temperatre T eff (eq. ). The view factor F acconts that a collector with a slope partially sees the sky and partially sees the grond, which is assmed to be at ambient temperatre (eq. 3). The heat transfer coefficient of the PVT collector cover cover is calclated with (eq. 4). 3 (,3 ( T T ) + 7, ) + (,83 4, ) conv glass amb 3 radiation glass ( T + T ) ( T T ) σ ε + T eff glass ( F ) F Tsky + T amb ( cos β ) eff glass eff (eq. ) (eq. ) (eq. ) F.5 + (eq. 3) T cover glas d glass d foil d n λglass λ foil λn (eq. 4) Tcell cover + Teff radiation + Tamb conv + + (eq. 5) cov er radiation conv 3. Determination of internal thermal condctance from thermal measrement The direct measrement of the internal heat transfer coefficient int between the absorber (cell) and the flid is particlarly for PVT collectors very difficlt. The assembly of sensors directly on the PV cells which form the absorber is hardly possible. Frthermore the determination of the internal heat transfer coefficient is not a part of the EN 975- performance test. Bt for the calclation of the electrical PV power the PV cell temperatre is essential. Hence, a calclation method for int is proposed by sing the data of the thermal performance test and integrated in the TRNSYS model. The int vale is approximately constant over all operation conditions of the collector. This assmption is valid for constant material data and flow rates, i.e. it may be sed, if the relevant temperatre and flow rate ranges are kept small. This is the case for nglazed collectors. In particlar, the int vale may be regarded as independent from ambient air speed. In contrary to a glazed collector the conversion factor of an nglazed collector is far more a fnction of the air speed. This air speed dependent conversion factor, of the thermal performance is derived from the EN 975 test (eq. 5, see also (Dffie & Beckman, 6)) nder steady state conditions, at a flid temperatre which eqals the ambient temperatre (eq. 6). The slope of the thermal performance crve b v,, which represents the collector heat losses, is given by the thermal performance crve (see eq. 5) and may be described with (eq. 7). Frthermore the collector efficiency factor F as a fnction of the loss coefficient and with it as a fnction of air speed is defined by (eq. 8), (Rockendorf, 995). η ( b ) α η (eq. 6), F

5 b v, F b + b F (eq. 7) loss, int (eq. 8) int + loss, With (eq. 6) to (eq. 8) the internal heat transfer coefficient can calclated by (eq. 9). int F F loss, bv, η α, α b α η v,, α α η ( b + b ) ( b ) (eq. 9) This procedre leads to a set of int vales for varying air speed levels. These vales shold be approximately identical. This reqirement may serve as a control algorithm, whether the collector parameters are appropriate. 4. Development and Validation Procedre The PVT collector model is developed and tested in TRNSYS on test rig measrements and validated on a measrement of a 4 m² PVT collector field in a heat pmp system with borehole heat exchanger over the period of one year. For parameterization of the model the thermal parameters are derived from a standardized thermal measrement according to EN 975- in open circit operation. The electrical parameters are derived from the manfactrer s data sheet for the sed PV modle. For the incident angle modifier of the electrical side data were taken from a measrement (Balenzategi, 4) of a standard PV-modle. After a plasibility check the same data were taken for the thermal incident angle modifier. The model was spplied with the measred meteorological data as inpts. In the pilot plant the simlation reslts are compared with daily yields over the period of one year. The test rig measrements are tested in minte yields over a period of hors. 4.. Qantifying of the validation reslts The deviation of thermal yield Q and electrical yield E el is calclated with the formla in (eq. ). It shows the relative deviation between simlated and measred thermal and electrical yield. ΔQ ( Q Q ) ( E E ) sim Q meas meas ΔE el el,sim E el,meas el,meas (eq. ) In addition to that, the relative sqare deviation (Hilmer, 999) for thermal and electrical yield was calclated by (eq. ). The term x meas is the mean vale of the measred yield over all intervals of the measred period. For the validation in the pilot plant over the period of one year, the deviation of daily total yields and the mean vale of all daily yields over this year were sed. V N N i ( x x ) sim meas xmeas (eq. ) 4.. Test rig measrements for plasibility checks For the test rig plasibility check dring the development, the PVT collector was measred with electrical power prodction by connection to a conventional small power inverter for single PV modles. Dring the measrements the PVT collector was operated in the point of maximm power. The measred data were recorded in time steps of 3 s. The ncertainty of measrement for thermal yield has been determined to ±.5% and for the electrical yield within ±.6%, not taking into accont the ncertainty of the data logger (which is small) and the failre of the MPP tracker. In TRNSYS the otpt was simlated in time steps of minte. For that prpose the collector model was parameterized like the measred PVT collector and the measred data were sed as model inpts. For the plasibility check on test rig a time period of 3 measring days with total hors with dynamic weather

6 conditions were available. The deviation for thermal yield between simlation and measrement is -3.% and.5% for relative sqare deviation. Fig. 4. shows the reslts for a time period of 7 h on Jly 3, 9. 3 P el in W measrement 6 Q se in W 4 simlation 5 G in W/m² 5 9: : 3: 5: time (date: Jly 3, 9) Fig. 4.: Measred and simlated electrical power and heat flow rate and radiation over a period of 7 hors According to these reslts the thermal heat flow rate is reprodced with good accracy, only with an acceptable restriction in the dynamic behavior for qick changes of radiation. Here, greater deviations cased by the thermal collector capacity occr. In contrast, the electrical power is mch less sensitive to the ambient conditions and shows a good dynamic behavior. The inflence of the cell temperatre on the electrical power is sally by 4% per K so that the power is primarily dependent on the radiation. Fig. 4. shows a systematic deviation between measred and simlated electrical power, which is the highest at the middle of the day. This indicates a systematic measrement error, which may be cased by the MPP tracker. In addition to that, the model was parameterized with the PV modle datasheet and not with the measred electrical properties of the PV modle in se Validation on pilot plant measrements The PVT collector model is validated against measrements on a 4 m² PVT collector field. The collector field is integrated in a heat pmp system with borehole heat exchanger and consists of m² inslated and m² not inslated PVT collectors of the same type. Inslated means in this case, that the back side of the PVT collector is eqipped with an additional 3 cm thick mineral wool layer nder the flid system. For the validation measrement data were sed for the period of one year with the data of global and infrared radiation in collector area, air speed, the temperatres of ambient air and collector in- and otlet, flid mass flow, electrical voltage and crrent and operating condition of the electrical inverter. For the electrical validation only daily periods were sed, where array shading and low inverter power (less than % of rated power) cold be exclded. The thermal validation incldes all measred data. The measred yields in the period of one year was for the thermal yield kwh/m² and for the electrical yield 74.3 kwh/m² (not inslated) and 74.4 kwh/m² (inslated). The ncertainty of the measrement for thermal yield has been determined to ±4.% and for electrical yield to ±.6% for the not inslated and ±.7% for the inslated PVT collector field. The diffse radiation on collector srface was calclated with the Perez model in the TRNSYS type 6. The simlation time step was minte eqal to the interval of the averaged measred data. Fig. 4. displays the simlated and measred daily yields from April 9 to March. The deviation in the yearly thermal yield is +.7% and for the relative sqare deviation 6.3%. For the electrical yield the deviation is +.% for

7 the inslated and +.4% for the not inslated PVT collector field. The relative sqare deviation of the electrical yield is.7% for the inslated and 3.4% for the not inslated PVT collector field. E el in kwh/m²d Q se in kwh/m²d measrement simlation Apr May Jn Jl Ag Sep Oct Nov Dec Jan Feb Mar month (April 9 - March ) Fig. 4.: Daily measred and simlated thermal and electrical yield of the pilot plant over the period of one year In addition to that fig. 4.3 displays the monthly simlated and measred thermal and electrical yields over the same period. A good accordance between monthly simlated and measred yields may be seen, so that the developed model allows the simlation of thermal and electrical yield with high accracy, for monthly and yearly periods. E el in kwh/m²d Q se in kwh/m²d measrement simlation Apr May Jn Jl Ag Sep Oct Nov Dec Jan Feb Mar month (April 9 - March ) Fig. 4.3: Monthly measred and simlated thermal and electrical yield of the pilot plant over the period of one year 5. Conclsion A new model for liqid cooled nglazed PVT collectors is presented, that combines the characteristic thermal and electrical performance models. The model was implemented in the simlation program TRNSYS. In contrast to existing models the new model reqires only standard performance data, which are determined according to EN 975- and EN The model incldes the effects of air speed dependency, long-wave radiation to sky, thermal collector capacity and condensation effects on collector srface. Frthermore, the model was extended by an approach to determine the PV cell and modle srface temperatre. Therefore the internal heat transfer coefficient between PV cells and flid is sed. A method to calclate this internal heat transfer coefficient from the standard thermal performance data is proposed. The model was tested on test rig measrements and validated against a measrement of a pilot system over a

8 period of one year. The following table displays the validation reslts. The deviations between simlated and measred thermal and electrical yield vales are given as relative deviations of total yields and as relative sqare deviations (see chapter 4.). Tab. : Deviations of simlated and measred thermal and electrical yields (relative deviation and relative sqare deviation) Thermal Yield Electrical Yield inslated not inslated Measrement data from Q V E V E V pilot plant +.7% 6.3% +.%.7% +.4% 3.4% It may be conclded, that the new model for nglazed PVT collectors allows the simlation of thermal and electrical yield with a high accracy, if applied in long-term (e.g. monthly or annal) simlations. Only simlations with a high resoltion of time and in cases of highly dynamic changes of inpt vales vales lead to significant differences. This model allows the evalation of the electrical yield inflenced by the cooling effect in comparison to a standard PV modle. 6. Nomenclatre Symbol Qantity Unit A Area m² b Heat loss factor of PVT-collector W m - K - b Air speed dependent heat loss factor J m -3 K - b Air speed dependent conversion factor s m - c L Specific heat capacity of ambient air kj kg - K - c T Temperatre coefficient for electrical power of PV-modle % K - d Diameter m h v Evaporation of water kj kg - I Crrent A k dif Incident angle correction factor for diffse radiation - k,beam Incident angle correction factor for beam radiation - Le Lewis nmber (Le.87 for water vapor in air) - m mass flow rate kg h - p Air pressre mbar p s Water vapor satration pressre mbar R D Gas constant of water (R D.464 kj kg - K - ) kj kg - K - R L Gas constant of air (R L.87 kj kg - K - ) kj kg - K - air speed m s - loss heat loss coefficient W m - K - absorption coefficient - emission coefficient - Incident angle Stefan Boltzmann constant ( W m - K -4) W m - K -4 sbscripts amb Ambient loss losses beam Beam OC Open circit DC Direct crrent ot otlet dif Diffse SC Short circit in Inlet sky Sky l Longitdinal t transverse 7. References Balenzategi, J.L., Chenlo, F., 5. Measrement and analysis of anglar response of bare and encapslated silicon solar cells. Solar Energy Materials & Solar Cells Volme 86 Isse. Bertram, E., et al., 9. Soil regeneration by nglazed solar collectors in heat pmp systems. In ISES Solar World Congress 9 renewable energy shaping or ftre. Johannesbrg, Soth Africa: International Solar Energy Society.

9 Dffie, J.A. & Beckman, W.A., 6. Solar Engineering of Thermal Processes 3rd Afl., Wiley. EN 975- DIN Detsches Institt für Normng e.v., 6. Thermische Solaranlagen nd ihre Bateile, Kollektoren, Teil : Prüfverfahren, Detsche Fassng EN 975-:6, Beth Verlag, Berlin. EN 694- DIN Detsches Institt für Normng e.v., 7. Photovoltaische Einrichtngen - Teil : Messen der photovoltaischen Strom/Spannngskennlinien (IEC 694-:6); Detsche Fassng EN 694-:6, Beth Verlag, Berlin. Hilmer, F., et al., 999. Nmerical soltion and validation of a dynamic model of solar collectors working with varying flid flow rate. Solar Energy Vol. 65, No. 5. Rockendorf, G., et al., 995. Methods to determine the internal heat transfer coefficient between absorber and flid of solar collectors. In Proceedings. Solar World Congress ISES. International Solar Energy Society. Wagner, A., 6. Photovoltaik Engineering, Handbch für Planng, Entwicklng nd Anwendng,., überarbeitete Aflage, Springer Verlag.